Question

You own two small gift shops, one in City A and one in City B. You are interested in which city spends more on Valentine's day gifts. So you test the claim that the mean amount spent in City A is less than the mean amount spent in City B

You wish to test the claim that the mean amount spent in City A is less than the mean amount spent in City B at a significance level of α=0.10  

You obtain the following two samples of data from each city. Each data point is the amount of a Valentine's Day gift purchase.

City A	City B
72.4 68.6 45.2 66.7 81.0 60.3 79.2 76.9 58.5 81.0 47.5 78.4 59.4	48.1 62.4 76.1 85.5 61.5 56.8 88.5 81.2 63.7 53.1

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the mean amount spent in City A is less than the mean amount spent in City B.
   • There is not sufficient evidence to warrant rejection of the claim that the mean amount spent in City A is less than the mean amount spent in City B.
   • The sample data support the claim that the mean amount spent in City A is less than the mean amount spent in City B.
   • There is not sufficient sample evidence to support the claim that the mean amount spent in City A is less than the mean amount spent in City B.

Answer 1

The statistical software output for this problem is:

From above output:

Test statistic = -0.6649

p - Value = 0.4739

greater than α

Fail to reject the null

There is not sufficient sample evidence to support the claim that the mean amount spent in City A is less than the mean amount spent in City B.